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CONFUSING KASTA TOMB AND GEOMETRY
By Prof. Lefteris Kaliambos ( Λευτέρης Καλιαμπός) T. E. Institute of Larissa Greece November 2014 Despite the various speculations about the history and the dimensions of the Amphipolis tomb my discovery of the Alexandrian stadion (d = 1 stadion = 157.5 m) of the circular base of the Kasta hill reveals all the secrets of the monument, which give us the sacred numbers of Babylonians like 7 and 12 used in the ancient astronomy. Surprisingly I discovered also that Dinocrates used earlier the same numbers 7 and 12 for planning the perimeter P of the ancient Alexandria in Egypt, since I found that P = 7X12 = 84 stadia. Such important discoveries lead to the conclusion that Alexander the Great ordered his architect Dinocrates for planning in Amphipolis a monument as a miniature of Alexandria in Egypt . CONFUSING HISTORY OF THE KASTA TOMB Archaeologists unearthing a burial site at Amphipolis in northern Greece have made an extremely important discovery which however leads to several speculations. Professor M.Tiverios believes the tomb belonged to an important figure from Amphipolis dating back to the last quarter of the Fourth Century BC , like the navarch Nearchus. According to the History of Greek people ( Ekdotike Athenon, Volume Δ, page 14 ) Androsthenes, Laomedon and Nearchus Alexander the Great’s three admirals are closely connected to Amphipolis. Androsthenes and Laomedon were born there, while Nearchus was either born or exiled in Amphipolis. In 335 BC Alexander’s army from Amphipolis marched out against to north Thrace , while in 334 BC Alexander sailed from Amphipolis to Asia. On the other hand Professor Theodoros Mavrogiannis believes that the Kasta tomb belongs to Hephaestion and claims that the tomb was built by order of Alexander himself. Note that Archaeologists have made a number of important discoveries on the site since August 2014. Apart from the sheer size of the monument, which experts say bears the handprint of Dinocrates of Rhodes, the chief architect of Alexander the Great. However the archaeologist Olga Palagia suspects that the Kasta tomb might not be Greek at all-but Roman. Nevertheless, since the circular base o the Amphipolis tomb has a very great diameter of one stadion (see my AMPHIPOLIS TOMB AND SCIENCE ) some archaeologists believe that it is the tomb of Alexander the Great. Whereas it is almost certain that the tomb of Alexander the great is located in Alexandria, since people such as Julius Caesar have visited his burial site. Some, however, insist that his bones were moved to Amphipolis by Olympias, while others argue that it is a cenotaph including Roxana and her son Alexander. Roxana the wife of Alexander became the mother of Alexander’s son in 323 BC after Alexander had died. Roxana fled to Epirus in order to be saved by his descendants, and later went to Amphipolis, where she was murdered by Cassander in 310 BC. CONFUSING GEOMETRY OF THE TOMB LEADS TO COMPLICATIONS Unfortunately for providing the dimensions of the Kasta tomb the architect Michael Lefantzis , who is a member of the Amphipolis excavation team, has not related the circular base of the Amphipolis tomb to the unit length (one stadion) of the Hellenistic period (one stadion = 157.5 m). So in the absence of such a detailed knowledge although the perimeter (C ) of the circular base of the tomb measured outside the surrounding wall is 497 meters the architect M. Lefantzis wrote that the diameter (d) of the Amphipolis tomb is d = 158.4 m which cannot be related to the standard number π = 3.1416 proposed theoretically by Archimedes. For example the ratio C/d gives a smaller number than the standard number π = 3.1416 as C/d = 497/158.4 = 3.1376 < π = 3.1416 Also under the same wrong diameter (d =158.4 m ) in several articles we see a perimeter C= 500 m which gives another number greater than the standard number π as C/d = 500/158.4 =3.1566 > π =3.1416 It is very important to notice that the height (T) of the Kasta hill is 22.5 m, while the total height ( H ) of the lion with its foundation base is H = (8 +5.2)= 13.2 meters. Here we clear that the height of the lion alone is 5.37 meters, while the height of the statue with its base is about 8 meters. ( See in the “Kasta tomb-WIKIPEDIA ” that the lion of Amphipolis is an 8 meters tall statue). In order to compare the height of the lion of Amphipolis to the height of the lion of Chaeronea we see that the total height of the lion of Chaeronea is greater (9.1 meters), because the height of the lion alone is 6.1 m (see it in the “Chaeronea-WIKIPEDIA ”), while the height of base is 3 meters. (See it in the “ ΛΕΩΝ ΤΗΣ ΧΑΙΡΩΝΙΑΣ ΒΟΙΩΤΙΑ ”). Surprisingly in the Amphipolis tomb archaeologists have found also the foundation base with a height of 5.2 meters. This means that the total height H of the lion of Amphipolis (located on the top of the Kasta hill) was greater than the height of the lion of Chaeronea since in Amphipolis the total height of the lion is H = 8 + 5.2 = 13.2 meters. Unfortunately M. Lefantzis in order to provide an harmonic relation between the total height (H ) of the lion of Amphipolis and the wrong diameter (d =158.4 m) of the circular base of the Kasta hill increased arbitrarily the total height from the correct H = 13.2 m to the wrong H =15.84 m, so that the ratio being 10 times smaller than the wrong diameter (d = 158.4 m). Such a confusion is obvious also in the horizontal and vertical illustrations of two diagrams in which the surrounding wall is 497 m with a wrong diameter of 158.4 m . Also for providing a perfect harmony in the diagrams the lion seems to cover incorrectly the half size of the wrong H = 15.84 m. ( See it in the “Kasta tomb- WIKIPEDIA”). DETAILED GEOMETRY REVEALS THE SECRETS OF THE TOMB WHICH GIVE US THE SACRED NUMBERS 7 AND 12 OF BABYLONIANS After a careful analysis I discovered that a perfect harmony should be given by using the height H = 13.2 or the detailed H = 13.125 meters which leads to the well known number TWELVE of Babylonians . Indeed when we compare it with the correct diameter d of the circular base (d = 1 stadion = 157.5 meters) we get 1 stadion/13.125 = 157.5/13.125 = 12 Then following the same method I discovered that also the height of the hill (T = 22.5 m ) leads to the second well known number SEVEN of Babylonians. In this case when we compare it with the correct diameter (d) of the circular base of the tomb, we get 1 Stadion/ T = 157.5 m/22.5 m = 7 It is of interest to notice that the number TWELVE was very important in the ancient astronomy because it expresses the full moons in a year. Historically, month names are names of moons (lunations, not necessarily full moons) in lunisolar calendars. Since the introduction of the solar Julian calendar in the Roman Empire, and later the Gregorian calendar worldwide, month names have ceased to be perceived as "for the moon names". Also the number SEVEN is the result of the phases of the moon. While Pythagoreans believed that the number SEVEN is the harmony of the seven notes in music. Evidence of continuous use of a seven-day week appears with the Jews during the Babylonian Captivity of the 6th century BC. Both Judaism (based on the Genesis creation narrative) and ancient Babylonian religions used a seven-day week. CONFUSING RELATIONS FOR COMPARING THE CIRCULAR BASE OF THE TOMB WITH A HYPOTHETICAL PERIMETER OF THE ANCIENT ALEXANDRIA LEAD TO COMPLICATIONS Unfortunately another confusion about the comparison of the wrong diameter (d) of the Amphipolis tomb and the perimeter P of the walls of the ancient Alexandria in Egypt is provided by the same architect of the excavation team in Amphipolis, because the architect suggested arbitrarily that the perimeter P of the walls in Alexandria was 100 times greater than the diameter (d=158.4 m). That is P/d = 15,840 /158.4 = 100 On the other hand in other articles he seems to hypothesize that the diameter ( D) of the walls of the ancient Egypt is D = 15.84 Km. (See in the “Parapolitika.gr , Ακριβής μικρογραφία της Αλεξάνδρειας , ο τύμβος της Αμφίπολης ”). That is D/d = 15,840/158.4 = 100 DETAILED'' RELATIONS BASED ON THE ALEXANDRIAN UNIT LENGTH (STADION) AND ON ANCIENT DIAGRAMS REVEALED THAT ''THE PERIMETER P OF THE ANCIENT ALEXANDRIA IS P = 7X12 = 84 STADIA At the beginning such a discovery of the perimeter of the ancient Alexandria seemed to be a very difficult problem, because today we have not any detailed knowledge about the ancient Alexandria. It is of interest to note that Alexandria was founded by Alexander the Great in 331 BC (the exact date is disputed) as Ἀλεξάνδρεια (Aleksándreia). Alexander's chief architect for the project was Dinocrates. Ancient accounts are extremely numerous and varied, and much influenced by subsequent developments. One of the of more sober descriptions, given by the historian Arrian, tells how Alexander undertook to lay out the city's general plan, but lacking chalk or other means, resorted to sketching it out with grain. A number of more fanciful foundation myths are found in the Alexander Romance and were picked up by medieval historians Nevertheless to avoid also the confusion of the architect M. Lefantzis one can see the plan of the ancient Alexandria (c. 30 BC) according to Otto Puchstein (c.1890). Using the scale: 1:100,000 we see that the ancient Alexandria in Egypt had the shape not of a circle but of a rather parallelogram, because Alexandria was located along a narrow land between the Mediterranean sea and the lake Mareotis. ( See the plan of Aexandria in the “History of Alexandria-WIKIPEDIA ”). After a detailed analysis I found that the walls had a perimeter P of the ancient Alexandria given by P = 13230 m = 13230/157.5 = 84 stadia Of course such a number seemed to be not important because it is not related with the number 10 of the modern decimal system . But when I multiplied the sacred numbers 7 and 12, surprisingly I found that P = 7X12 = 84 stadia Such a surprising tels us that 'the Amphipolis tomb is a miniature of the ancient Alexandria '''because it includes the same sacred numbers 7 and 12 of Babylonians. After this important discovery I compared also the well known HEPTASTADION ( a mole of seven stadia) in Alexandria with the Ampfipolis diameter d = 1 stadion = 177.5 m and I found that the ratio gives exactly the number 7. On this basis I analysed carefully the length of the Heptastadion shown in the map with the diagram of Otto Puchstein and I found that it was constructed by using not the Attic stadion ( 1 stadion = 185 m ) but the unit of length of the Hellenistic period (Alexandrian stadion = 157.5 meters). '''THE SACRED NUMBERS 7 AND 12 OF ALEXANDRIA AND THE AMPHIPOLIS TOMB ALONG WITH THE NUMBER π DID MUCH FOR ΤΗΕ PROGRESS OF ASTRONOMY ' In my paper AMPHIPOLIS TOMB AND ASTRONOMY I emphasize that Dinocrates for defining the perimeter of the Amphipolis tomb used the radius r = d/2 = 0.5 St = 157.5/2 = 78.75 m. So he was able to define the circle. Nevertheless If Dinocrates for calculating the circular are applied the following formula , we would find in the Amphipolis tomb a perimeter circle ( C) as C = 3.16 X 157.5 = 497.7 m Of course this is the perimeter of the circular base of the Amphipolis tomb measured outside the surrounding wall. For practical purposes the papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area (E ) of a circle with a diameter (d ) by applying the following formula E = (256/81)( d2/4 ) = 3.16Xd2/4 Here the number 3.16 is the approximate value for π. However here one sees that my discovery of the one stade in Amphipolis tomb supports not only the idea that Eratosthenes used the stade of the Hellenistic period but also the idea that the practical number π = 3.16 was used also before the time of Archimedes. Moreover the numbers 7 and 12 of Babylonians which were related with the perimeter of the walls in ancient Alexandria are used also here for the construction of the Amphipolis tomb. Such numbers used in the astronomy of Babylonians were of course responsible for the progress of astronomy in Alexandria developed by the great Greek mathematicians and astronomers. In my book COSMOGONY (2012) which is in the library of Larissa I pointed out that the measurement of the diameter D of our Earth by Eratosthenes opened new horizons for the astronomy. So the Greek mathematician and astronomer Aristarchus o Samos ( 310 BC-230 BC) under the measurement of the diameter D of the Earth found that the Sun is greater than the Earth. So Aristarchus developed the heliocentric system by saying that the Earth moves around the Sun because it is smaller than it. The heliocentric system was successfully revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy, with Kepler's laws, and Isaac Newton gave a correct explanation based on laws of gravitational attraction and dynamics. Particularly after many centuries (1687) Newton based on the heliocentric system discovered the law of universal gravity according to which a gravitational force acting at a distance is equal to the inertial force due to the orbital velocity of the Earth measured always with respect to the Sun. However later (in 1905 and 1916) Einstein’s contradicting theories of relativity led to serious complications because he believed incorrectly that the Earth and the Sun are equivalent systems. Category:Fundamental physics concepts